With a little care and gentle cleaning, the natural fibers of wicker furniture will keep looking good for years.
The term "wicker" actually refers to the technique of bending and weaving a material such as paper, rattan, bamboo, other grasses, or thin woods such as willow branches. Look carefully at your pieces for identifying properties -- the characteristic rings on bamboo, the rough bark of a tree branch -- to determine what your wicker furniture is made from.
To clean dirty wicker that's made of bamboo, rattan, or willow, brush off or vacuum as much of the surface dirt as you can. Then wash it with a soft brush and soapy water to which you've added one or two teaspoons of ammonia. Rinse well and let the piece dry outdoors in the sun.
To clean wicker made from twisted paper or grasses, simply wipe with a damp cloth.
To restore unpainted or natural wicker to its warm glow, rub it with linseed oil (available at art supply stores), then gently wipe off the excess. Be sure to let it dry for several days before sitting on freshly oiled chairs, or set cushions on the seat and seatback to keep from getting oil on your clothing.
If you have an antique piece of wicker, just clean the surface carefully but don't attempt to change it. Painting antique natural wicker, for example, will greatly reduce its value.